Research On Image Reconstruction Iterative Algorithm For Electrical Capacitance Tomography Based On Modified Implicit Landweber

Electrical Capacitance Tomography is usually referred to as "ECT" technique.This technology can collect the capacitance signal between the external plates of the medium through the "capacitance sensor" and the "measurement and data acquisition system",and then use the appropriate algorithm to reconstruct the distribution of the dielectric constant in the medium based on the obtained capacitive signal information.The image reconstruction algorithm used in ECT is a crucial factor influencing the solution of the inverse ECT problem.In this paper,in order to obtain better ECT image reconstruction effect,a kind of image reconstruction algorithm for Electrical Capacitance Tomography based on modified implicit type Landweber and a Huang clan correction image reconstruction algorithm for Electrical Capacitance Tomography are presented respectively on the basis of analyzing the basic principle of ECT image reconstruction.The simulation results show that these two algorithms provide new routes for solving the inverse problem of electrical capacitance tomography.This article can be summarized as the following three parts:(1)In combination with the ECT inverse problem solving mathematical model,the ECT image reconstruction principle and the ill-posedness of the ECT inverse problem are analyzed in detail.And linear back projection algorithm,steepest descent method,Polynomial Acceleration Algorithm,conjugate gradient algorithm and Tikhonov regularization method are introduced.These are typical and commonly used methods in ECT image reconstruction.In addition,the ECT system components are briefly described.(2)An ECT image reconstruction algorithm based on modified implicit Landweber is proposed for solving the 'soft-field' nature and the ill-posed problem in ECT technology.Based on the study of ECT image reconstruction mathematical model,this paper deduces the solving formula to solve the ECT image reconstruction problem,and further analyzes the convergence of this algorithm.In order to verify the effectiveness of the ECT image reconstruction algorithm,four different flow patterns of ECT image reconstruction simulation experiments were performed.From the results of simulation experiments,this method has a very good guarantee on the accuracy and speed of the experiment.For extremely low laminar flow,low laminar flow and core flow,the error rate of image reconstruction of this method is lower than that of LBP,classic Landweber,CG and SD.(3)In view of the ill-posed problem of inverse ECT problem,a Huang clan correction image reconstruction algorithm for Electrical Capacitance Tomography is proposed on basis of the analysis of the basic principles of quasi-Newton algorithm.This algorithm combines the quasi-Newton condition to derive the Huang family correction formula for constructing theHesse matrix approximation of the ECT image reconstruction objective function,and then derives the iterative solution formula for ECT image reconstruction based on the quasi-Newton algorithm's solution principle,and passes the ECT Image reconstruction simulation experiments to explore the feasibility of this algorithm for ECT image reconstruction.Simulation results show that the proposed algorithm works better than LBP,Landweber and SD methods on all experimental flow patterns.Compared with the modified implicit Landweber method,the method has better imaging effect on the laminar laminar flow and columnar flow.Also,the image error rate of this method on the very low laminar flow is the lowest among all methods.